Journal
INTERNATIONAL JOURNAL OF CONTROL
Volume 96, Issue 9, Pages 2374-2383Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207179.2022.2094837
Keywords
Reaction-diffusion equations; prescribed-time stabilisation; disturbances estimator; time-varying feedback gain; Neumann boundary control
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In this study, we investigate the Neumann boundary feedback stabilization for reaction-diffusion equations with matched boundary uncertainties. We propose a prescribed-time boundary control law by estimating the uncertainties within the prescribed time and utilizing backstepping transformation with a time-varying kernel. The Neumann boundary control is proven to be uniformly bounded.
We study the Neumann boundary feedback stabilisation for reaction-diffusion equations with matched boundary uncertainties (including internal uncertainty and external disturbance) within a prescribed time, where the convergence time is independent of initial conditions and can be prescribed a priori. We first estimate the uncertainties within the prescribed time by constructing an estimator and then propose the prescribed-time boundary control law by utilising backstepping transformation with a time-varying kernel. Neumann boundary control is verified to be uniformly bounded.
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